Computer



July 18, 1950 E. Ll HARDER 2,516,000

7 COMPUTER Filed June 3, 1948 2 Sheets-Sheet l flnalagy Sine Voltage WITNESSES: INVENTOR m Edwin Lflarden 2% F ATTORNEY Patented July 18, 1950 UNITED STATES PATENT OFFICE COMPUTER Edwin L. Harder, Pittsburgh, Pa., assignor to Westinghouse Electric Corporation, East Pittsburgh, Pa., a corporation of Pennsylvania,

Application June 3, 1948, Serial No. 30,904

The use of electrical analogy types of computers inthe study of various physical problems has been known for the past several years.

state-conditions in power systems has been applied fairly extensively; and in recent years through the development of suitable excitation means for the analogy circuits such studies have been extended to transient problems not only. in the power transmission field mentioned but also in-other fields, moreimportantly among these be ing in the study of mechanical and electromechanical systems.

For the purposes of this disclosure, and without any-intention of limiting the scope of the teachings hereof, the discussions'hereinafter presented will be concerned with the study of ducing voltages corresponding-to, these various components are well covered in the above-mentioned patent of G. D. McCann, et al.,,and this invention is directed primarily to-an improved method and apparatus for producingcosine voltages in excitation systems-of the character mentioned.

Generally, it is an object of this invention to provide an improved type of electrical analogy computer.

A further general object of this invention is to-provide an improved type of excitation circuit for use in an electrical analogy type of computer.

More specifically stated, it is an object of this invention to provide. an excitation circuit for an electrical analogy type of computer embodying improved means for producing cosine voltages.

The foregoing statements are merely illustra- Theuse of such-a computer system in the study of steady tive-of the various aims-and objects of this invention. Other objects and advantages will become apparent upon a study of the following disclosure when considered in conjunction with the accompanying drawings, in which:

Fig. l diagrammatically illustrates an electrical analogy type of computer having an excitation circuit-forproducing sine voltages.

Fig. 2 is a graph illustrating a typical form of decaying amplitude sine voltage produced in the excitation network of Fig. 1.

Fig. 3 diagrammatically illustrates an electrical analogy type of computer having an exciting circuit for producing sine and cosine voltages of decaying-amplitude.

Fig. 4 is a graph of typical sine and cosine voltages produced in the excitation network of i Fig. 5 is a diagrammatic showing of an electrical analogy computer having an excitation network embodying the principles of this invention.

Fig. 6 is asimilar type of computer having an excitation network which is a variation of that shown in Fig, 5, and

Figs. 7, 8 and 9 demonstrate the application of this invention in the solution of a typical generator torque problem.

In Figs. 1 and 3 of the drawings typical computer. networks areillustratedof a type disclosed and claimed in U. S. Patent 2,420,891, issued May 20, 1947 and assigned to the same assignee as this invention. The circuits of Figs. 1 and 3 and their respective characteristic curves in Figs 2 and 4. are herein illustrated and discussed that the improvements afforded by this invention may be more readily understood.

In the study of most transient problems the cathode ray. oscilloscope usually aiforcls the best means of measuringthe quantities which are to be determined. Since this oscilloscope is primarily a, voltage measuring instrument, a frequently convenient analogy is that in which the desired force or torque in the mechanical system is proportional to a voltage in the electrical analogy circuit. In other analogies the current can just as readily be measured by taking a voltage drop across a resistor element in the analogy circuit. Thus the mass capacitance analogy might also be used.

The analogy circuitof Fig. 1 is based upon the mass-inductance analogy and'represents a simple three-mass system. For instance, that represented by a generator andtwo turbines for driving the generator connected along a common shaft-in which case the inductor IL is propor:

tional to the mass of the generator, the inductor 2L is proportional to the mass of the first turbine and the inductor 3L is proportional to the mass of-the second turbine. The capacitors l C and 2C, connected in parallel in the analogy network, are each inversely proportional to the spring constants of the shaft sections between the generator and the first turbine and thefirst and second:

turbines respectively. The voltages appearing across the respective capacitors EC and 2C upon the application of suitable excitation voltages to the analogy network are therefore proportional:-

to the peak stresses occurring inthe shaft for, a given operating condition and.maybeconven iently observed upon the screen of a cathode ray oscilloscope designated CRO in the drawing, se-

synchronous switch SS closes the common leg 'of the oscillator circuits and also of such size as ;to--"-permit the capacitors to become essentially lectively connected to measure the'voltages across the respective capacitors. Switches SSiiand SS1 respectively connected in series with resistors R6 and R1 across capacitors IC and 2C are provided to remove energy from thean'alogy ci'rcuit'during intervals between the applications of excitation thereto as will bedescribed more fully in connection with Fig. 9.

The excitation circuit in this case has ma been set up to represent any specific problem but is one which will produce sinusoidalvoltag s" of decaying amplitude of a type typicallyvrepre sentative of the components of air gap torque occurring in the generator upon short-circuit or :12

upon synchronization out of'ph ase. Each component of torque is represented in a voltage produced in an oscillator network in the excitation circuit. Four of these oscillator 'circuits'f are shown. These may produce voltages of various amplitude and of the same frequency or various frequencies depending upon the character of the particular quantities whichare to be electrically reproduced. For instance, the first oscillator circuit comprising the capacitor Cl, inductor Ll i and resistor RI may produce a voltage of given" amplitude and of fundamental frequency. The second oscillator circuit including the capacitor C2, the inductor L2 and the resistor R2 may produce a voltage of some harmonic-frequency, for instance, the second harmonic, The third oscillator circuit including the capacitor C3, the in--' ductor L3 and resistor R3 may produce a voltage of fundamental frequency'but: of opposite sense to that of the first oscillator circuit and similarly the fourth oscillator circuit including capacitor C4, inductor L4 and resistor R4 may produce a voltage of the second harmonic frequency but of opposite sense to that of the second oscillator circuit. The foregoing discussion is merely illustrative of the combinations which may be effected. It will be appreciated that each of the circuits above described may beof' different ire-I quencies and of various voltage magnitudes of may all be of the same frequency and i'zarious voltage magnitudes etc, depending upon the reg Each oscillator circuit includes a quirements. portion of the resistor Rand a'cornmon leg 'for each oscillator circuitis forrned bythe synchronous switch SS which operates to simul taneously open and close the oscillator circuits:

at a speed which is commensurate with the time constants of the respective circuitsand also of a speed to afford persistance of the image being viewed upon the screen of the cathode ray oscilloscope so as to aiforda standing reproduction of the transient phenomena being observed.

The oscillator circuits are each ccnnected to a charging circuit having a battery 13 as the common source of charging potential. Each chargfully charged during the period when the switch SS isopen. Thus the stored energy in each of ;the capacitors in the oscillator circuits is released in the oscillator circuit and the circuits oscillate after'closing of the synchronous switch substantially independently of the charging circuit associated therewith,

The particular turbine system under consideration is a lowloss'mechanical system. Thus the analogy'circuit must be a low loss electrical system. This is accomplished by utilizing high Q coils in the analogy circuit and in general keepingthe analogy circuit resistance low. For this reason in the particular type of circuit being considered the value of the resistor R as well as other components in the oscillator circuits of the network must-be kept as low as possible so- I that the internal impedance of the excitation network as viewed from the analogy network is a minimum, that interference with the analogy network for all practical purposes willbe negligible. The resistors RI through R4 may be actual physical resistors added in series in the various'oscillator circuits or may represent only" the lumped resistance of each'oscillator circuit due tothe resistive properties of the inductors and capacitors therein. SS6 and SS! and their respective series resistors are respectively connected across the capacitors lC'and 2C of the analogy circuitp Physically these switchesare connected mechanically with switch SS and operated therewith. The setting is such that upon closure of switch SS to initiate oscillation in the excitation circuits switches SS6 and SS! are opened. When switch SS opens to initiate charging in the excitation circuits switches SS6 and SS! close and 'short'circuit the components of the" analogycircuit and remove the residual electrical energy therefrom placing these circuits at rest in advance of the reapplication of excitation across resistor R.

"In Fig. 3, for the purpose of simplifying the illustration, the analogy circuit is represented in theform of a'block. The excitation circuit of Fig 3 is similar to that ofFig. 1 but in: addition in orporates means for producing" cosine voltages as well as sine voltages as generally char acte'rized by the graph of Fig. 4. The circuits in Fig. '3 involving the inductor Ll, capacitocCI, resistor RI, inductor L3, capacitor C3 and resistor R3 are the same as those bearing the same reference characters illustratedin Fig. 1

and the operation thereof will be understood in" connection with the discussion concerning Fig.1.

:The cosine voltages are produced in this instance across the inductors 2L and AL, now form'- ing apart of the impedance'Z corresponding to resistor R of Figure 1 in which the various oscillator voltages are accumulated to produce-the total voltage correspondin to total air gap torque. One oscillator circuit for producing the cosine voltages includes the capacitor C2, inductor L2 and resistor R2 and this circuit is Synchronous switches connected: along; a-tapped portion of the inductor 2L. A circuit for producing: a cosine function or opposite senseincludes the capacitor C4, inducto'r Lt and theresistor R4. and this circuit includes a. tapped: portion; of the inductor 1L forming a: part of the. impedance in which. the oscillator. voltages; are: combined; 'I-hese circuits, it will be: appreciated may'produce various relative magnitudes of voltages andvarions-irequem cies or the same frequency as the particular circumstances require; and eachischarged by means of its charging circuit connecting the capacitor therein across the battery 13. Upon charging of the capacitors inthe oscillator circuits in Fig. 3, closure of the synchronous switch SS results in a: discharge: of. these capacitors into the various oscillator circuits and since the voltage appear ing'. across: the. two inductors 2L and 4h of impedance Z is 90 displaced. in phase" with respect to the? voltage appearing across the resistor R at reference time zero when. oscillation is initiated; the separate components of sine and cosine volt ages are produced and these are combined in the over-all impedance Z to produce an excitation voltage E thereacrosswhich is applied to the analogy circuit.

While the'above'described method of producing the cosine voltages has been. used and has been found practicalfor most purposes, certain operational inconveniences are experienced in the use of excitation systems embodying this method for producing the cosine voltages. One such inconvenience resides in the fact that it isnot always feasible to obtain smooth variation of. the taps along the inductors 2L or. 4L. Additionally, the current in each. of the inductors 2L and 4L also flows through the resistor Rand produces an unwanted sine component therein. One method for eliminating the sine component produced by the cosine current is to proportion the current in the cosine oscillator circuits at amuch lower value. than that of the adjacent sine circuit so that the amount of unwanted sine component will be minimized. Another method is to balance out the sine component in an electrically opposed section of: the resistor R. Nevertheless, this is still difficult to accomplish accurately and the convenience of: uniform variations and ready manual manipulation by observing the oscillograph during test setup periods is lost.

According to this invention one method for minimizing the above problems; as illustrated in Fig; 5', utilizes the resistance.- R for both the sine and cosine components. In this embodiment the sine circuits include the components Lt, Cl, R! and L3; C3, R3 as in Figs. 1 and 3. These circuits-willaccordingly be. understood from the dismission of: Fig. 1. Inthis instance, however, in the cosine circuits, and with particular reierence to: the cosine circuit. including components C2, B2 and" R2, the inductor L2 is connected across the: battery B: by a synchronous switch SS2 during. periods when the various oscillator circuits are being charged. The same applies to the inductor. L4 appearing in the other osciiia tor circuit for producing cosine components of the opposite: polarity which additionally includes the capacitor C4 and resistor R4. Inductor M connected across the battery B by means of a synchronous switch SS4 during charging inter vals. The resistors 2B and 3Bv in the charging circuits for capacitors Ci and C3 in the voltage oscillator circuits are again of relatively high magnitude" to afiord substantial isolation of. the" charging circuits for the" sine voltage 05- 6 cillator' circuits when the synchronous switch SSI is closed but the requirements for the reisistors. IR and 4B are slightly different. It will bev remembered that the internal impedance of the excitation circuits as viewed from theanalogy circuit must be low to prevent interference with oscillation of the analogy circuit during periods when the excitation circuits are producing the voltage E. Thus, the inductors L2 and L4 must include only a. relatively few turns of wire to meet this condition. As a consequence, a rather large current is. required through these elements to produce the required ampere turns in the circuit. For. this reason the resistors IR and 4R in the respective cosine charging circuits must bekept small and toaiiord isolation of the charging circuits the synchronous switches SS2 and SS4 are provided to open the charging circuits during periods when the oscillator circuits are closed.

Each cosine oscillator circuit is provided with a synchronous switch, respectively designated SS3 and SS5 for the two circuits. The capacitors C2 and C4 in the respective cosine circuits nor mally'bloch the passage of direct current. However, upon application of the battery to the cosine circuit for building up ampere turns on inductors L2 and lt i, the direct current voltage is-not constant but builds up exponentially. Such a current would be passed by the capacitors and in the event of a closed connection to the resistor It would permit a current flow through the circuit network including the resistor R which may have a spurious effect in the function ofthe analogy circuit. If it is found that the effect of the charging current circulating through resistor R during the charging cycle is of negligible inrportance, then of course the synchronous switches SS3 and SS5 may be eliminated from the cosine circuits. In practice all synchronous switches are arranged along a common shaft with means being provided for adjusting the switch segments angularly about the shaft to effect any desired angular relation therebetween and means also being provided for individual adjustment of the brushes so that the on-off cycles of the switches can be adjusted to provide the desired switching characteristics.

In view of the fact that the inductors L2 and L4 are of low impedance since they have a relatively few number of turns, it will be appreciated that a fairly heavy current drain upon the source will occur upon closure of the switches SS2 and SS4. Practical considerations may make it nec essary therefore to provide each of the cosine charging circuits with a separate battery to provide the required charging current. However, a more practical approach to this problem appears in the preferred embodiment illustrated in Fig. 6.

In Fig. 6, the sine voltage oscillator circuits have been eliminated for the purpose of simplification. Here again the cosine voltage circuits embody, respectively, an inductor Ll, capacitor Cl, resistor Bi and capacitor C2, inductor L2 and resistor R2. However, in this instance the inductors are provided with additional exciting or primary windings PI and P2, respectively, having a large number of turns of small wire so that the desired ampere turns can be induced on these coils LI and LB witha small drain from the power supply. Each of the paired coil as sembliesPl, Li and P2, L2, it will be appreciated, respectively function as mutual inductors or, in effect; a transformer assembly so that the ampere turns of the primary ineach case are transferred inductively to the secondary circuits including the coils or inductors LI and L2.

As illustrated, the charging circuit including the two primaries PI and P2 is a series circuit including, the battery B, the resistor lR which now may be of relatively large magnitude, the two primaries PI and P2 and a synchronous switch SS. When the synchronous switch SS is closed as illustrated in the drawing, steady conditions are established with the cores of the mutual inductors excited but with no voltage on the capacitors CI and C2. When the synchronous switch opens the charging circuit at time equals zero, the ampere turns of the primary windings are instantly transferred inductively to their respective secondary windings LI and L2 in the cosine voltage oscillator circuits. In other words, a current is initiated at its peak value at time equals zero producing a cosine damped term. The series connection of these exciting coils PI and P2 avoids any coupling between the circuits through the exciting circuit after the commutator has opened. This makes possible the use of the convenient slid wire adjustment along the resistor R for determining the relative characteristics of the cosine voltages with only a moderate drain on the power supply. As in previous instances hereinbefore discussed the voltage appearing across the resistor R is applied to the analogy circuit.

The application of this electrical analogy computer in a particular problem is illustrated in Figs. '7 through 9 in which the problem is that of determining the transient torque on the turbine generator shaft illustrated in Fig. '7 when the generator is synchronized out of phase. In this problem the generator is given an inertia value I1, the turbine an inertia value I2 and the shaft a spring constant K all as illustrated in Fig. '7.

The torque developed in the rotor during synchronizing takes the form T=Ae Bc" cos wt-l-Cef sin wt (1) where A, B, and C are functions of the angle of synchronizing, where A, a and 'y are decrement factors. This torque acts on the mechanical system consisting of the generator rotor, the generator, the turbine shaft and the turbine.

The equations for dynamic equilibrium of the mechanical system are given by and where If a mass-inductance analogy is used, voltage will correspond to torque, current to velocity, and charge to displacement. A simple excitation circuit which will produce voltage components corresponding to the terms of the torque Equation (1) is shown in Figure 9.

The electrical analogy for the mechanical system is also shown in Fig. 9. The correspondence between the electrical analogy network of Fig. 9 and the mechanical system can be readily seen by writing the equations for dynamic equi-'- librium in terms of voltage and charge for the analogy network.

2 0=L%+% eqo Note the similarity between Equations (2) and (4.), and (3) and (5). The second term in Equations (4) and (5) represents the voltage drop across the capacitor CI, and since voltage is analogous to torque, gives directly the torque developed in the shaft. 7

The torque T given in Equation (1) represents the forcing function which excites the mechanical system. This may be writtenas a voltage E which is illustrated in the drawing as the voltage or forcing function which excites the electrical system and this voltage is to be produced across the resistor R forming a part of the excitation circuit. The characteristics of the separate voltages represented in the equation for the voltage shown are illustrated in Fig. 8 in which the ordinate represents voltage and the abscissa time. As is apparent from-the form of the mathematical expressions defining each of the voltages, these voltages are exponentially damped. The first voltage, namely Aeis a unidirectional component which is decreasing exponentially. This is illustrated by the graph so designated in Fig. 8. The second voltage Br cos wt may be considered as a fundamental frequency and of a sense relatively negative to that of the unidirectional component. This is the cosine'term and accordingly is displaced in phase from that of the component designated C'e sin of which is the third voltage. The addition of these curves represents the voltage E which is applied to the analogy network. The three circuits for producing the voltages are illustrated inthe excitation network of Fig. 9 wherein for an instantaneous condition each of the voltages is designated according to the expression appearing in the voltage equation. The unidirectional damped term is produced in the circuit including a capacitor Cl and resistor Hi. The cosine term is produced in the circuit including the secondary winding S3 of the transformer T3, the capacitor C3 and resistor R3 while the sine voltage is produced in the circuit including capacitor C2, inductor L2 and resistor R2. The power supply in this instance for the charging circuits is designated as a block labeled PS. For this particular problem the power supply may be any suitable source of unidirectional voltage. The charging current for the damped unidirectional voltage circuit and for the sine voltage circuit is applied, respectively, across capacitors Cl and 02. These charging circuits respectively include the resistors IR and 2R which serve to isolate the charging circuits when the synchronous switch SSi has closed the oscillating circuits. The charging circuit for the cosine voltage circuit includes a synchronous switch SS2, the primary P3 of the mutual inductor, T3 and the resistor 3B in a series loop across the power supply PS. As discussed in connection with Fig. 6, the inductor or secondary winding S3 forming a part of the cosine voltage oscillating circuit'ha's but a few turns of wire whereas the primary P3 of the mutual inductor T3 has a large number of turns=of small wire sothat-the required ampere turns can be produced with a small charging current. Here also the synchronous switches SS1, SS2 and SSS-are connected together to eifect opening and closing of the circuits of which they each form a part in suitable-time phase relation. in the arrangement illustrated in the drawing, switch SS2 is closed, switch SS! is open and switch SS6 is'closed. Thus the oscillator circuits are open and charging currents are flowing. In

the analogy circuit-the discharge circuit estab lished by switch SS6 completely removes energy from the analogy circuit. In the next instant switch SS2 opens, switch SS! closes and switch SS5 opens. Switch SS2 opens the cosine charging circuit and SS! completes the three oscillator circuits. Switch SS6 opens the discharge path in the analogy circuit. Thus simultaneously the three components of voltages shownin Fig. 8 are initiated. This corresponds to time zero in the graph of Fig. 8 and each of the element voltages as shown by the exponential terms in the equa tions are exponentially damped producing across the resistor 'R the excitation voltage E which is aal lllied to the analogy circuit. The forces acting upon the shaft connecting the turbine and the generator appear as voltages across the capacitor C and are traced on the screen of a cathode ray oscilloscope CRO. Due to the cyclic operation of switches SS] and SS2 in the excitation network, the excitation voltage E is repeatedly applied to the analogy network at sufiiciently small intervals to produce a standing wave of shaft stress on the cathode ray oscilloscopewhere it may be leisurel studied or photographed for thepurpose of future recordand the switch SS5 completely removes energy from the analogy circuit in the interval between excitation applica tions thereto. 7

It will also be appreciated from a study of the excitation networkcf Fig. 9 that the manner in which the combination of the voltages of the three separate oscillator units is accomplished .correspondsexactly to that indicated in the equation of the voltages. Thecosine term is negative in the equation and in the excitation circuit is combined with the other two voltages in an opposite sense since the point of connection of the cosine circuit with the resistor R is on the oppo site side of thecommon leg of theexcitation circuit along the resistor R from the points of connection of :the two remaining circuits. It will be noted that the common leg .or branch includes the synchronous switch, one side of which is connected to the resistor R, and the other side of Which is connected to a common terminal of the power supply which applies a reference voltage to the synchronousswitch tap on the resistor R. Thus, voltages appearing along resistor R are relatively positive or negative with respect'to this pointdependingupon thepoint of application of the particular circuit producingsuch-voltage.

Although this invention has been illustrated in connection with a single practical application, namely that of the turbine generator of Fig. '7, it will be appreciated that the teachings hereof are by no means limited to such an application and it is therefore intended that the foregoing disclosure shall be considered only as illustrative of the fundamental principles of this invention.

I claim as my invention: 1. In an electrical analyzer network having an analogy circuit which is the electrical counterpart of a=system to be analyzed, an excitation circuit for producing voltages representative of the quantities affecting the said system comprising, incombination, a transformer having a high impedance primary winding and a low impedance secondary winding, an oscillator circuit including said low impedance secondary winding, a charging circuit including said high impedance primary winding and impedance means having a low impedance with respect to said analogy circuit for connecting said oscillator circuit and said analogy circuit.

2. In an electrical analyzer network having an analogy circuit which is the electrical counterpart of a system to be analyzed, an excitation circuit for producing voltages representative of the quantities affecting the said system comprising,in combination, mutual inductor means havingprimary and secondar windings, the primary winding having a higher number of turns than the secondary winding, a charging-circuit including said primary winding, an oscillator circuit includsaid secondary winding, switching means for opening and closing said charging circuit, and impedance means having a low impedance with respectto said analogy circuit for connecting said oscillator circuit and said analogy circuit.

In an electrical analyzer network having an analogy circuit which is the electrical counterpart of a system to be analyzed, an excitation circuit for producing voltages representative of the quantities affecting the said system comprising, in combination, mutual inductor means having primary and secondary windings, the primary winding having a higher number of turns than the secondary winding, a charging circuit including saidlprimary winding, an oscillator circuit including said secondary winding, switching means in .eaclroi the charging circuits and the oscillator circuit for alternately opening and closing the cha-rging circuit and the oscillator circuit, and

impedance means having a low impedance with respect to the analogy circuit for connecting said oscillator. circuit and said analogy circuit.

'4. In an electrical analyzer network having an analogy circuit which is the electricalcounterpart :of a system to be analyzed, an excitation circuit iorproducing voltages representative of the quantitles affecting the said system comprising, in combination, mutual inductor means havingpri- .mary and secondary windings, the primary winding having a higher number of turns thanthe secondarywinding, a charging circuit including said primary winding, an oscillator circuit including said secondary winding, switching means for opening and closing the oscillator circuit, resistor means in the charging circuit, said resistor means being of suf icientl high resistance to efiectively isolate the charging circuit from-the oscillator circuit when said switching means closes said oscillatorcircult, and impedance means having a low impedance with respect to the impedance of said analogy circuit for connecting said oscillator circuitand said analogy circuit.

5. Inch electrical analyzer network having an analogy circuit which is the electrical counterpart of a system to be analyzed, an excitation circuit for producing voltages representative of the quantities affecting the said system comprising, in combination, a plurality of mutual inductors each having primary and secondary windings, a charging circuit connecting said primary windings in series, a plurality of oscillator circuits each including a secondary winding of said mutual inductors, impedance means connected with all of .said oscillator circuits and havinga low impedof a system to be analyzed, an excitation circuit for producing voltages representative of the quantities affecting the said system comprising, in combination, a first electrical circuit including an inductor and a capacitor, mutual inductor means having a primary winding and a secondary wind- .ing, a second electrical circuit including said secondary winding and a capacitor, circuit means for simultaneously energizing said capacitor of said first electrical circuit and said primary winding, impedance means connecting said first and second electrical circuits, switching means for opening and closing said circuit means and said first and said second electrical circuits in predetermined time phase relation, said impedance means being constructed and arranged for connection to said analogy circuit.

7. In an electrical analogy type of computer, the combination of, an analogy circuit which is the counterpart of a system to be analyzed, mu-

tual inductor means having a primary and a secondary winding, said primary winding having a greater number of turns than said secondary winding, an oscillator circuit including said secondary winding, circuit means connecting said oscillator circuit to said analogy circuit, and a charging circuit connected to said primary windmg.

8. In an electrical analogy type of computer, the combination of, an analogy circuit which is the electrical counterpart of a system to be analyzed, mutual inductor means having a primary winding and a secondary winding, said primary winding having a greater number of turns than said secondary winding, an oscillator circuit including said secondary winding, circuit means connecting the oscillator circuit to said analogy circuit, a source of electrical ener y, and a cyclically operated switch connecting said primary winding to said source of electrical energy.

9. In an electrical analogy type of computer, the combination of, an analogy circuit which is the electrical counterpart of a system to be analyzed, mutual inductor means having a primary and a secondary winding, said primary winding having a greater number of turns than said secondary winding, an oscillator circuit in-.- cluding said secondary winding, circuit means connecting said oscillator circuit to said analogy circuit, a charging circuit connected to said primary winding, and switching means for alternately opening and closing said charging circuit and said oscillator circuit.

10. An excitation network for producing cosine voltages comprising, in combination, inductor means, an oscillator circuit including said inductor means, impedancemeansforming a part of said oscillator circuit and across which said cosine voltages appear, a charging circuit connected to said inductor means, and switching means for alternately opening, and closing said charging circuit and said oscillator circuit.

, 11. An excitation circuit for producing cosine voltages, comprising, in combination, mutual inductor means having a primary and asecondary winding, said primary winding having a greater number of turns than said secondary winding, an oscillator circuit including said secondary winding, impedance means forming a part of said oscillator circuit and across which said cosine voltages appear, and charging circuit means for energizing said primary winding.

12. Apparatus as set forth in claim 11 in which said charging circuit means comprises a synchronous switch for intermittently opening-and closing the charging circuit.

13. An excitation circuit for producing cosine voltages comprising, in combination, mutual inductor means having a primary and a secondary winding, said primary winding having a greater number of turns than said secondary winding, an oscillator circuit including said secondary winding, impedance means forming a part of said oscillator circuit and across which said cosine voltages appear, a charging circuit connected to said primary winding, and switching means for alternately opening and closing said charging circuit and said excitation circuit.

14. Circuit means for producing cosine voltages comprising, in combination, at least two mutual inductors each having a primary winding and a secondary winding, the primary windings of each mutual inductor having a greater number of turns than the secondary winding thereof, a pair of oscillator circuits, each including one of said secondary windings so that each secondary winding forms a part of an oscillator circuit, said oscillator circuits having a common circuit branch, impedance means connected with each of said oscillator circuits to form a part thereof, and charging circuit means connecting said primary windings in series, said cosine voltages appearing across said impedance means.

I 15. Apparatus as set forth in claim 14 in which said charging circuit comprises switching means for intermittently opening and closing the charging circuit.

EDWIN L. HARDER.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Name Date McCann May 20, 1947 Number OTHER REFERENCES 

